Most math papers have few figures, if any, although sometimes a well-chosen figure can be a tremendous help in understanding mathematical concepts. Does anyone have any examples of notable uses of figures in mathematical writing and/or texts that make great use of figures/diagrams/illustrations?

I am a huge fan of the drawings of Anatoly Fomenko (for some of his drawings, see here; for a description of his odd historical theories, see his wikipedia pages here and here).

In particular, his book "Algorithmic and Computer Methods for Three-Manifolds" with Matveev (which really has nothing to do with computers) is IMHO one of the best intro books on 3-manifolds available largely because of its drawings. The mathscinet review of the Russian version is worth reading; see

When I was an undergraduate I read the book Intuitive Topology by Prasolov. It's a wonderful illustrated guide to low-dimensional topology (mostly knots/links and surfaces). If I recall correctly, almost all of the "proofs" are by pictures.

Edward Tufte's books are quite beautiful, though they do not focus so much on mathematical figures/diagrams per se. However, via Tufte, I did come across this version of Euclid's Elements by Oliver Byrne, which presents the propositions and proofs of the Elements using colored diagrams and symbols. I'm not sure whether Byrne's edition is clearer or better to learn from than the original Euclid, but it sure is pleasing to look at.

Knots, links, braids, and 3-manifolds, by Prasolov and Sossinsky (you can look at it on Google books) essentially has a picture on every page. They are very pretty.

Indra's pearls by Mumford, Series, and Wright has some breath-taking pictures. There are also cartoons by Gonick, which improves any book. Here's the copy at Google books.

Edit: A topological picturebook, by Francis is wonderfully illustrated. There are directions for reproducing the figures, as well as their mathematical meaning. Chapter eight of the book deals with the figure eight knot. :)

It's a great image, but a somewhat provocative placement, making the frontispiece of “Undergraduate Commutative Algebra” a shibboleth which will delight the initiate but baffle a newcomer to Algebraic Geometry. But then, Miles Reid doesn't tend to shy away from being provocative...
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Peter LeFanu LumsdaineSep 22 '10 at 14:32

H.S.M. Coxeter's books include Regular Polytopes. This book deals with the classification of regular polytopes. In this book there are Coxeter diagrams which are closely related to Dynkin diagrams. In his works are many diagrams,figures and illustrations. They influenced M.C Escher. Many of Escher's works reflect his ideas. In 1996 Coxeter published a paper on one of these "Circle Limit III." For more information see here and here.